Instructions: Remove four strips of zest from one of the grapefruit. Each strip should be about 4 inches long and 1 inch wide; avoid the bitter white pith. Set the strips aside. Juice both the grapefruit; you should have about 2 cups juice. Set the juice aside.

In a medium saucepan, combine the sugar and water over high heat. Stir occasionally until the sugar is completely dissolved and the syrup is simmering, about 5 minutes. Remove from the heat.

Combine the warm syrup with the zest, grapefruit juice, strawberry purée, vodka, and lemon juice. Set aside for 30 minutes to 1 hour, according to taste: the grapefruit flavor strengthens as it sits. For faster freezing, transfer the cooled mixture to the refrigerator to chill there first.

Strain the mixture and then freeze it in an ice-cream maker, following the manufacturer's instructions.